{"paper":{"title":"Coorbit spaces with voice in a Fr\\'echet space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Demetrio Labate, Ernesto De Vito, Filippo De Mari, Gabrielle Steidl, Gerd Teschke, Stefano Vigogna, Stephan Dahlke","submitted_at":"2014-02-17T07:34:21Z","abstract_excerpt":"We set up a new general coorbit space theory for reproducing representations of a locally compact second countable group $G$ that are not necessarily irreducible nor integrable. Our basic assumption is that the kernel associated with the voice transform belongs to a Fr\\'echet space $\\mathcal T$ of functions on $G$, which generalizes the classical choice $\\mathcal T=L_w^1(G)$. Our basic example is $ \\mathcal T=\\bigcap_{p\\in(1,+\\infty)} L^p(G)$, or a weighted versions of it. By means of this choice it is possible to treat, for instance, Paley-Wiener spaces and coorbit spaces related to Shannon w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3917","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}